If the clips that come with the sink aren't long enough to clamp it to the slab, they generally also offer longer ones as an option. The caulk helps to keep crud from accumulating under the lip, water from leaking through, and to act as a second means of holding it in place (in addition to the clamps).

Depending on the stone, some caulks can stain the stone. You may want to try it on a scrap or maybe the underside of the slab to see how yours reacts.